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Polynomials over commutative rings added #714

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Mar 10, 2022
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Polynomials over commutative rings added #714

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Polynomials over commutative rings added
AkermanRydbeck Feb 4, 2022
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32 changes: 32 additions & 0 deletions Cubical/Algebra/CommRing/Instances/Polynomials.agda
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{-# OPTIONS --safe #-}

module Cubical.Algebra.CommRing.Instances.Polynomials where

open import Cubical.Foundations.Prelude
open import Cubical.Algebra.CommRing
open import Cubical.Algebra.Polynomials

private
variable
ℓ : Level


ℙ : (R : CommRing ℓ) → CommRing ℓ
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ℙ R = (PolyMod.Poly R) , str
where
open CommRingStr (snd R)
str : CommRingStr (PolyMod.Poly R)
CommRingStr.0r str = PolyMod.0P R
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CommRingStr.1r str = PolyMod.1P R
CommRingStr._+_ str = PolyMod._Poly+_ R
CommRingStr._·_ str = PolyMod._Poly*_ R
CommRingStr.- str = PolyMod.Poly- R
CommRingStr.isCommRing str = makeIsCommRing (PolyMod.PolyIsSet R)
(PolyMod.Poly+Assoc R)
(PolyMod.Poly+Rid R)
(PolyMod.Poly+Inverses R)
(PolyMod.Poly+Comm R)
(PolyMod.Poly*Associative R)
(PolyMod.Poly*Rid R)
(PolyMod.Poly*LDistrPoly+ R)
(PolyMod.Poly*Commutative R)
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